"the circulation of the matter of the universe around the zenith seen by observers on a merry-go-round produces a field somewhat like the magnetic field produced by the circulation of electricity in the coils of an electromagnet. It is this Gravitomagnetic field that in the merry go round frame of reference produces the effects that in more conventional frames of reference are attributed to centrifugal force."

He goes on to say that, because of this, in general relativity we can not distinguish whether we are in a rotating laboratory or not.

This seems to be a bold, and wrong, acceptance of a very strong version of Mach's principle that

"all centrifugal effects are caused by the gravitational effects of the rotating stars when viewed from the rotating reference frame."

Weinberg's account seems contrary to modern views on Mach's principle. Yes, there is the Lense-Thirring effect and frame dragging, but that is a long way from saying that all inertial effects in a rotating reference frame are caused by the motion of the surrounding matter in the universe.

Can't we determine whether we are in a spinning spaceship or not (using centrifugal and inertial effect), without reference to the distant stars? Wouldn't Weinberg's claim mean that if we let the mass of the surrounding universe approach zero, the centrifugal effect in the rotating lab frame would go to zero as well?

In short, is Weinberg wrong about Mach's principle in general relativity here?

$\begingroup$@Countto10 Yes, I read it and it seems to say that Weinberg is wrong. I would have thought Weinberg knew better. He wrote a very famous book on GR. It's hard for me to believe he is this wrong so I'm questioning my own understanding.$\endgroup$
– David Santo PietroOct 11 '17 at 20:02

$\begingroup$What if there are no stars in the universe?$\endgroup$
– safesphereOct 11 '17 at 20:12

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$\begingroup$Weinberg book is very old, my only thought is that, given the title, he was trying to be inclusive and possibly, given his reputation, he was trying to get discussion going again on a topic he had a fondness for. If he has not covered it since, I guess he has moved on.$\endgroup$
– user171879Oct 11 '17 at 20:19

1 Answer
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Brans-Dicke's original paper on their scalar-tensor version of GR starts with an exploration of this question, and I highly recommend reading it - it's a wonderful example of how to write a science paper that just about anyone could understand

In my reading they basically suggest Mach is wrong, at least about the source of the "field". They give the example of someone in a cube who leans out the window and shoots a rifle tangentially to the cube. This will cause the cube to spin, and thus should produce centripetal forces. Yet according to Mach, the source of this is the "background", which in this case is a single 22 bullet. How is it this could have such an effect, compared to, say, the mass of the walls of the cube?

So the problem, if you see it that way, exists, but they suggest Mach's solution is wrong.

$\begingroup$I just took a brief look at Barns and Dicke paper. However, according to your explanation, I think there may be a fundamental misconception about Mach's principle in Barns-Dicke example. According to Mach's principle, you are not allowed to imagine a 22-caliber rifle or any laboratory with massive walls in an empty space (the background) because, according to Mach, if you eliminate all masses from the universe except a few number of objects (lab & rifle & bullet), these object would become massless because inertial mass is affected by the global distribution of matter.$\endgroup$
– Mohammad JavanshiryJan 22 at 21:59

$\begingroup$Therefore, the gyroscope, contrary to what claimed by Barns & Dicke, seems not to be rotating relative to the walls of the lab (linear and angular momentum are all zero). I think that Mach's principle implicitly states that it is not eligible to use traditional physical laws in an empty space (universe).$\endgroup$
– Mohammad JavanshiryJan 22 at 22:16

$\begingroup$Nice article reference! Thanks, it is a gem.$\endgroup$
– David Santo PietroMay 15 at 16:20